Properties

 Label 2.13.ah_bm Base Field $\F_{13}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{13}$ Dimension: $2$ L-polynomial: $( 1 - 4 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ Frobenius angles: $\pm0.312832958189$, $\pm0.363422825076$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 110 33660 5239520 823996800 137389054550 23260576584960 3936690829551590 665461638360921600 112458674518542740960 19005016038068177934300

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 197 2380 28849 370027 4819034 62737591 815785921 10604807500 137858870957

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ae $\times$ 1.13.ad and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.ab_o $2$ 2.169.bb_to 2.13.b_o $2$ 2.169.bb_to 2.13.h_bm $2$ 2.169.bb_to
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.ab_o $2$ 2.169.bb_to 2.13.b_o $2$ 2.169.bb_to 2.13.h_bm $2$ 2.169.bb_to 2.13.aj_bs $4$ (not in LMFDB) 2.13.ad_i $4$ (not in LMFDB) 2.13.d_i $4$ (not in LMFDB) 2.13.j_bs $4$ (not in LMFDB)